Kāma is a special seal that serves as a unique “backup” or memory card containing an Ōtsutsuki’s biological data. The sole purpose of the seal is to be embedded into the body of a compatible vessel. Afterwards the Kāma will gradually overwrite the vessel's genetic setup until they transform into a perfect Ōtsutsuki body.
Should the Ōtsutsuki die, their soul will migrate to the vessel (or one of their vessels if they have numerous), and when the Kāma completes, the Ōtsutsuki will reincarnate through their body, completely replacing the vessel. In the interim, the vessel can learn to activate the Kāma seal and utilise a portion of the Ōtsutsuki's power and abilities, and if reincarnation has not yet been achieved, the dead Ōtsutsuki can even manifest and take control over the vessel’s body.
So now we get to the Red Kama. This is achieved when an unsuitable vessel survives the ritual of the otsutsuki being reincarnated, however, producing a unique variant of the seal called the Red Kāma. Such individuals are unable to serve as a receptacle for the Ōtsutsuki's soul and thus cannot be used for the process of reincarnation, but retain its other traits, gaining tremendous power and even being able to transform into a completely new Ōtsutsuki themselves.